Question 1 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic. Z = -2.55 Z = -0.85 Z = -1.05 Z = -1.20 Question 2 If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to 39. 38. 19. 18. Question 3 Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of rands): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? R1,447.8 R180.975 R143.042 R8 Question 4 TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample size 211 100 Mean SSATL Score 65.75 79.83 Population Std. Dev. 11.07 6.41 Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ? Paired t test pooled-variance t test for the difference between two means F test for the ratio of two variances Z test for the difference between two proportions Question 5 TABLE 9-7 A major home improvement store conducted its biggest brand recognition campaign in the company’s history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who “like the ads a lot.” A study of 1,189 adults who viewed the ads reported that 230 indicated that they “like the ads a lot.” The percentage of a typical television advertisement receiving the “like the ads a lot” score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of “like the ads a lot” for the company’s ads is less than 0.22) at a 0.01 level of significance. Referring to Table 9-7, the null hypothesis will be rejected if the test statistics is greater than 2.3263. less than 2.3263. greater than -2.3263. less than -2.3263. Question 6 In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are n – 1. n1 + n2 – 1. n1 + n2 – 2. n – 2. Question 7 Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test. s12 = 4 s22 = 6 n1 = 16 n2 = 25 df = 41 df = 39 df = 16 df = 25 Question 8 If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s = 0.05, the critical value of t will be (tick made by mistake) 2.7969. 2.7874. 2.4922. 2.4851. Question 9 If the p-value is less than ? in a two-tail test, the null hypothesis should not be rejected. the null hypothesis should be rejected. a one-tail test should be used. no conclusion should be reached. Question 10 In testing for differences between the means of two related populations, the null hypothesis is H0 : ? D = 2. H0 : ? D = 0. H0 : ? D < 0. H0 : ? D > 0. Question 11 TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Student Exam score Before Course (1) Exam Score After course (2) 1 530 670 2 690 770 3 910 1000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 Referring to Table 10-5, the number of degrees of freedom is 14. 13. 8. 7. Question 12 TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Student Exam score Before Course (1) Exam Score After course (2) 1 530 670 2 690 770 3 910 1000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 Referring to Table 10-5, the value of the standard error of the difference scores is 65.027. 60.828. 22.991. 14.696. Question 13 The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region should she use? Reject H0 if t < -2.3263. Reject H0 if t < -2.5758. Reject H0 if t > 2.3263. Reject H0 if t > 2.5758. Question 14 An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be R1,000. A random sample of 50 individuals resulted in an average income of R15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than R100? n = 1537 n = 385 n = 40 n = 20 Question 15 Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of rands): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield X ? = 180.975 and S= 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments. R180.975 ± R94.066 R180.975 ± R99.123 R180.975 ± R116.621 R180.975 ± R119.586 Question 16 How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X ? = 52, S = 22. Using the sample information provided, calculate the value of the test statistic. t = (52 – 60)/22 t = (52 – 60)/(22/100) t = (52 – 60)/(22/1002) t = (52 – 60)/(22/10) Question 17 Which of the following would be an appropriate null hypothesis? The mean of a population is equal to 55. The mean of a sample is equal to 55. The mean of a population is greater than 55. Only The mean of a population is equal to 55. and The mean of a population is greater than 55. are appropriate. Question 18 In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are n – 1. n1 + n2 – 1. n1 + n2 – 2. n – 2. Question 19 The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make? Reject H0. Accept H0. Fail to reject H0. We cannot tell what her decision should be from the information given. Question 20 The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: tick made by mistake H0 :? ? 30 versus H1 :? < 30. H0 :? ? 30 versus H1 :? > 30. H0 :X ? ? 30 versus H1 :X ? < 30. H0 :X ? ? 30 versus H1 :X ? > 30. Question 21 TABLE 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Student Exam score Before Course (1) Exam Score After course (2) 1 530 670 2 690 770 3 910 1000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 Referring to Table 10-5, the value of the sample mean difference is ________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course. 0 50 68 400 Question 22 TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: X ?G = 35 months, SG2 = 900 Metropolis: X ?M = 50 months, SM2 =1050 Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01? My notes are not very clear , I THINK it is this sign between the t and the z. The tick in the column is made by mistake. t ? Z = -1.96 t ? Z = ±1.96 t ? Z = -2.080 t ? Z = -2.33 Question 23 TABLE 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below. Hypothesized Difference 0 Level of significance 0.05 Population 1 Sample Sample size 18 Sample Mean 48266.7 Sample Standard Deviation 13577.63 Population 2 Sample Sample Size 12 Sample Mean 55000 Sample Standard Deviation 11741.29 Difference in Sample Means -6733.3 t- Test Statistic -1.40193 Lower-Tail Test Lower Critical value -1.70113 p-value 0.085962 Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is: 0.0860 -1.4019 -1.7011 -6,733.33 Question 24 A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X ? = R50.50 and S2 = 400. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain’s new store in the mall assuming that the amount spent follows a normal distribution. R50.50 ± R9.09 R50.50 ± R10.12 R50.50 ± R11.00 R50.50 ± R11.08 Question 25 TABLE 10-11 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let n1 and n2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. Referring to Table 10-11, what is/are the critical value(s) when performing a Z test on whether population proportions are different if ? = 0.05? ± 1.645 ± 1.96 -1.96 ± 2.08 Question 26 TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: X ?G = 35 months, SG2 = 900 Metropolis: X ?M = 50 months, SM2 =1050 Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means? -8.75 -3.69 -2.33 -1.96 Question 27 How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X ? = 52, S = 22. Suppose the alternative we wanted to test was H1 : ? < 60. State the correct rejection region for ? = 0.05. Reject H0 if t > 1.6604. Reject H0 if t < -1.6604. Reject H0 if t > 1.9842 or Z < -1.9842. Reject H0 if t < -1.9842. Question 28 Suppose we want to test H0 :? ? 30 versus H1 : ? < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1? X ? = 28, S = 6 X ? = 27, S = 4 X ? = 32, S = 2 X ? = 26, S = 9 Question 29 TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: X ?G = 35 months, SG2 = 900 Metropolis: X ?M = 50 months, SM2 =1050 Referring to Table 10-4, what is a point estimate for the mean of the sampling distribution of the difference between the 2 sample means? -22 -10 -15 0 Question 30 TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: X ?G = 35 months, SG2 = 900 Metropolis: X ?M = 50 months, SM2 =1050 Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means? 4.06 5.61 8.01 16.00 Question 31 TABLE 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an mean of 257.3 W. Referring to Table 9-3, the parameter of interest is the mean power consumption of the 20 microwave ovens. the mean power consumption of all such microwave ovens. 250. 257.3. Question 32 A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The p-value associated with the test statistic in this problem is approximately equal to: 0.0100 0.0051 0.0026 0.0013 Question 33 In testing for differences between the means of two independent populations, the null hypothesis is: H0 :? 1 - ? 2 = 2. H0 :? 1 -? 2 = 0. H0 :? 1 - ? 2 > 0. H0 :? 1 -? 2 < 2. Question 34 The statistical distribution used for testing the difference between two population variances is the ________ distribution. t standardized normal binomial F Question 35 TABLE 10-11 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let 1 and 2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. Referring to Table 10-11, what is/are the critical value(s) when testing whether population proportions are different if = 0.10? ± 1.645 ± 1.96 -1.96 ± 2.08 Question 36 TABLE 9-4 A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision. Referring to Table 9-4, the appropriate hypotheses are: H0 :? = 7.4 versus H1 :? ? 7.4 H0 :? ? 7.4 versus H1 :? > 7.4 H0 :? ? 7.4 versus H1 :? < 7.4 H0 :? > 7.4 versus H1 :? ? 7.4 Question 37 Which of the following would be an appropriate alternative hypothesis? The mean of a population is equal to 55. The mean of a sample is equal to 55. The mean of a population is greater than 55. The mean of a sample is greater than 55. Question 38 TABLE 10-4 A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham: X ?G = 35 months, SG2 = 900 Metropolis: X ?M = 50 months, SM2 =1050 Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05? I am not sure what the sign is between the t and the Z as it is very unclear on my original sheet. It looks like the alpha sign that has a line underneath it. T ? Z = -1.645 T ? Z = ±1.96 T ? Z = -1.96 T ? Z = -2.080 Question 39 A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence? 105 150 420 597 Question 40 A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. State the test of interest to the rental chain. H0 : ? ? 0.32 versus H1 : ? > 0.32 H0 :? ? 0.25 versus H1 : ? > 0.25 H0 :? ? 5,000 versus H1 :? > 5,000 H0 :? ? 5,000 versus H1 :? > 5,000 Question 41 TABLE 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an mean of 257.3 W. Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer’s claim appears reasonable are: H0 : ? > 250 versus H1 : ? ? 250 H0 : ? ? 250 versus H1 :? < 250 H0 : ? ? 250 versus H1 :? > 250 H0 : ? ? 257.3 versus H1 :? < 257.3 Question 42 Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test. s12 = 4 s22 = 6 n1 = 16 n2 = 25 sp2 = 6.00 sp2 = 5.00 sp2 = 5.23 sp2 = 4.00 Question 43 If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to 39. 38. 19. 18. Question 44 The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make? There is not sufficient evidence that the mean age of her customers is over 30. There is sufficient evidence that the mean age of her customers is over 30. There is not sufficient evidence that the mean age of her customers is not over 30. There is sufficient evidence that the mean age of her customers is not over 30. Question 45 How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X ? = 52, S = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60. H0 :? ? 60 and H1 :? > 60. H0 :?? 60 and H1 :? < 60. H0 :X ? ? 60 and H1 :X ? < 60. H0 :X ? = 52 and H1 :X ? ? 52. Question 46 TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample size 211 100 Mean SSATL Score 65.75 79.83 Population Std. Dev. 11.07 6.41 Referring to Table 10-1, what is the value of the test statistic? -14.08 -11.8092 -1.9677 96.4471 Question 47 A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The value of the test statistic in this problem is approximately equal to: 2.80 2.60 1.94 1.30 Question 48 An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be R1,000. A random sample of 50 individuals resulted in an average income of R15,000. What is the upper end point in a 99% confidence interval for the average income? R15,052 R15,141 R15,330 R15,364 Question 49 If an economist wishes to determine whether there is evidence that mean family income in a community exceeds R50,000 either a one-tail or two-tail test could be used with equivalent results. a one-tail test should be utilized. a two-tail test should be utilized. None of these. Question 50 TABLE 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Japanese Sample size 211 100 Mean SSATL Score 65.75 79.83 Population Std. Dev. 11.07 6.41 Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers. H0 : ? A - ? J ? 0 versus H1 : ? A - ? J < 0 H0 : ? A - ? J ? 0 versus H1 : ? A - ? J > 0 H0 : ? A – ? J = 0 versus H1 : ? A – ? J ? 0 H0 : X ? A – X ? J ? 0 versus H1 : X ? A – X ? J ? 0

A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.

Z = -2.55

Z = -0.85

Z = -1.05

Z = -1.20

Question 2

If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to

39.

38.

19.

18.

Question 3

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of rands): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

R1,447.8

R180.975

R143.042

R8

Question 4

TABLE 10-1

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

American Japanese

Sample size 211 100

Mean SSATL Score 65.75 79.83

Population Std. Dev. 11.07 6.41

Referring to Table 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

Paired t test

pooled-variance t test for the difference between two means

F test for the ratio of two variances

Z test for the difference between two proportions

Question 5

TABLE 9-7

A major home improvement store conducted its biggest brand recognition campaign in the company’s history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who “like the ads a lot.” A study of 1,189 adults who viewed the ads reported that 230 indicated that they “like the ads a lot.” The percentage of a typical television advertisement receiving the “like the ads a lot” score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of “like the ads a lot” for the company’s ads is less than 0.22) at a 0.01 level of significance.

Referring to Table 9-7, the null hypothesis will be rejected if the test statistics is

greater than 2.3263.

less than 2.3263.

greater than -2.3263.

less than -2.3263.

Question 6

In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are

n – 1.

n1 + n2 – 1.

n1 + n2 – 2.

n – 2.

Question 7

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test.

s12 = 4 s22 = 6

n1 = 16 n2 = 25

df = 41

df = 39

df = 16

df = 25

Question 8

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample s = 0.05, the critical value of t will be (tick made by mistake)

2.7969.

2.7874.

2.4922.

2.4851.

Question 9

If the p-value is less than ? in a two-tail test,

the null hypothesis should not be rejected.

the null hypothesis should be rejected.

a one-tail test should be used.

no conclusion should be reached.

Question 10

In testing for differences between the means of two related populations, the null hypothesis is

H0 : ? D = 2.

H0 : ? D = 0.

H0 : ? D < 0.

H0 : ? D > 0.

Question 11

TABLE 10-5

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Student Exam score

Before Course (1) Exam Score

After course (2)

1 530 670

2 690 770

3 910 1000

4 700 710

5 450 550

6 820 870

7 820 770

8 630 610

Referring to Table 10-5, the number of degrees of freedom is

14.

13.

8.

7.

Question 12

TABLE 10-5

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Student Exam score

Before Course (1) Exam Score

After course (2)

1 530 670

2 690 770

3 910 1000

4 700 710

5 450 550

6 820 870

7 820 770

8 630 610

Referring to Table 10-5, the value of the standard error of the difference scores is

65.027.

60.828.

22.991.

14.696.

Question 13

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region should she use?

Reject H0 if t < -2.3263.

Reject H0 if t < -2.5758.

Reject H0 if t > 2.3263.

Reject H0 if t > 2.5758.

Question 14

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be R1,000. A random sample of 50 individuals resulted in an average income of R15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than R100?

n = 1537

n = 385

n = 40

n = 20

Question 15

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of rands): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield X ? = 180.975 and S= 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

R180.975 ± R94.066

R180.975 ± R99.123

R180.975 ± R116.621

R180.975 ± R119.586

Question 16

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X ? = 52, S = 22. Using the sample information provided, calculate the value of the test statistic.

t = (52 – 60)/22

t = (52 – 60)/(22/100)

t = (52 – 60)/(22/1002)

t = (52 – 60)/(22/10)

Question 17

Which of the following would be an appropriate null hypothesis?

The mean of a population is equal to 55.

The mean of a sample is equal to 55.

The mean of a population is greater than 55.

Only The mean of a population is equal to 55. and The mean of a population is greater than 55. are appropriate.

Question 18

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are

n – 1.

n1 + n2 – 1.

n1 + n2 – 2.

n – 2.

Question 19

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make?

Reject H0.

Accept H0.

Fail to reject H0.

We cannot tell what her decision should be from the information given.

Question 20

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: tick made by mistake

H0 😕 ? 30 versus H1 😕 < 30.

H0 😕 ? 30 versus H1 😕 > 30.

H0 :X ? ? 30 versus H1 :X ? < 30.

H0 :X ? ? 30 versus H1 :X ? > 30.

Question 21

TABLE 10-5

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Student Exam score

Before Course (1) Exam Score

After course (2)

1 530 670

2 690 770

3 910 1000

4 700 710

5 450 550

6 820 870

7 820 770

8 630 610

Referring to Table 10-5, the value of the sample mean difference is ________ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.

0

50

68

400

Question 22

TABLE 10-4

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01? My notes are not very clear , I THINK it is this sign between the t and the z. The tick in the column is made by mistake.

t ? Z = -1.96

t ? Z = ±1.96

t ? Z = -2.080

t ? Z = -2.33

Question 23

TABLE 10-2

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Hypothesized Difference 0

Level of significance 0.05

Population 1 Sample

Sample size 18

Sample Mean 48266.7

Sample Standard Deviation 13577.63

Population 2 Sample

Sample Size 12

Sample Mean 55000

Sample Standard Deviation 11741.29

Difference in Sample Means -6733.3

t- Test Statistic -1.40193

Lower-Tail Test

Lower Critical value -1.70113

p-value 0.085962

Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is:

0.0860

-1.4019

-1.7011

-6,733.33

Question 24

A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X ? = R50.50 and S2 = 400. Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain’s new store in the mall assuming that the amount spent follows a normal distribution.

R50.50 ± R9.09

R50.50 ± R10.12

R50.50 ± R11.00

R50.50 ± R11.08

Question 25

TABLE 10-11

A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let n1 and n2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

Referring to Table 10-11, what is/are the critical value(s) when performing a Z test on whether population proportions are different if ? = 0.05?

± 1.645

± 1.96

-1.96

± 2.08

Question 26

TABLE 10-4

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?

-8.75

-3.69

-2.33

-1.96

Question 27

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X ? = 52, S = 22. Suppose the alternative we wanted to test was H1 : ? < 60. State the correct rejection region for ? = 0.05.

Reject H0 if t > 1.6604.

Reject H0 if t < -1.6604.

Reject H0 if t > 1.9842 or Z < -1.9842.

Reject H0 if t < -1.9842.

Question 28

Suppose we want to test H0 😕 ? 30 versus H1 : ? < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1?

X ? = 28, S = 6

X ? = 27, S = 4

X ? = 32, S = 2

X ? = 26, S = 9

Question 29

TABLE 10-4

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is a point estimate for the mean of the sampling distribution of the difference between the 2 sample means?

-22

-10

-15

0

Question 30

TABLE 10-4

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is the estimated standard error of the difference between the 2 sample means?

4.06

5.61

8.01

16.00

Question 31

TABLE 9-3

An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an mean of 257.3 W.

Referring to Table 9-3, the parameter of interest is

the mean power consumption of the 20 microwave ovens.

the mean power consumption of all such microwave ovens.

250.

257.3.

Question 32

A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The p-value associated with the test statistic in this problem is approximately equal to:

0.0100

0.0051

0.0026

0.0013

Question 33

In testing for differences between the means of two independent populations, the null hypothesis is:

H0 😕 1 – ? 2 = 2.

H0 😕 1 -? 2 = 0.

H0 😕 1 – ? 2 > 0.

H0 😕 1 -? 2 < 2.

Question 34

The statistical distribution used for testing the difference between two population variances is the ________ distribution.

t

standardized normal

binomial

F

Question 35

TABLE 10-11

A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let 1 and 2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

Referring to Table 10-11, what is/are the critical value(s) when testing whether population proportions are different if = 0.10?

± 1.645

± 1.96

-1.96

± 2.08

Question 36

TABLE 9-4

A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.

Referring to Table 9-4, the appropriate hypotheses are:

H0 😕 = 7.4 versus H1 😕 ? 7.4

H0 😕 ? 7.4 versus H1 😕 > 7.4

H0 😕 ? 7.4 versus H1 😕 < 7.4

H0 😕 > 7.4 versus H1 😕 ? 7.4

Question 37

Which of the following would be an appropriate alternative hypothesis?

The mean of a population is equal to 55.

The mean of a sample is equal to 55.

The mean of a population is greater than 55.

The mean of a sample is greater than 55.

Question 38

TABLE 10-4

A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05? I am not sure what the sign is between the t and the Z as it is very unclear on my original sheet. It looks like the alpha sign that has a line underneath it.

T ? Z = -1.645

T ? Z = ±1.96

T ? Z = -1.96

T ? Z = -2.080

Question 39

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

105

150

420

597

Question 40

A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. State the test of interest to the rental chain.

H0 : ? ? 0.32 versus H1 : ? > 0.32

H0 😕 ? 0.25 versus H1 : ? > 0.25

H0 😕 ? 5,000 versus H1 😕 > 5,000

H0 😕 ? 5,000 versus H1 😕 > 5,000

Question 41

TABLE 9-3

An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an mean of 257.3 W.

Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer’s claim appears reasonable are:

H0 : ? > 250 versus H1 : ? ? 250

H0 : ? ? 250 versus H1 😕 < 250

H0 : ? ? 250 versus H1 😕 > 250

H0 : ? ? 257.3 versus H1 😕 < 257.3

Question 42

Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test.

s12 = 4 s22 = 6

n1 = 16 n2 = 25

sp2 = 6.00

sp2 = 5.00

sp2 = 5.23

sp2 = 4.00

Question 43

If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to

39.

38.

19.

18.

Question 44

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make?

There is not sufficient evidence that the mean age of her customers is over 30.

There is sufficient evidence that the mean age of her customers is over 30.

There is not sufficient evidence that the mean age of her customers is not over 30.

There is sufficient evidence that the mean age of her customers is not over 30.

Question 45

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:

X ? = 52, S = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

H0 😕 ? 60 and H1 😕 > 60.

H0 :?? 60 and H1 😕 < 60.

H0 :X ? ? 60 and H1 :X ? < 60.

H0 :X ? = 52 and H1 :X ? ? 52.

Question 46

TABLE 10-1

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

American Japanese

Sample size 211 100

Mean SSATL Score 65.75 79.83

Population Std. Dev. 11.07 6.41

Referring to Table 10-1, what is the value of the test statistic?

-14.08

-11.8092

-1.9677

96.4471

Question 47

A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The value of the test statistic in this problem is approximately equal to:

2.80

2.60

1.94

1.30

Question 48

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be R1,000. A random sample of 50 individuals resulted in an average income of R15,000. What is the upper end point in a 99% confidence interval for the average income?

R15,052

R15,141

R15,330

R15,364

Question 49

If an economist wishes to determine whether there is evidence that mean family income in a community exceeds R50,000

either a one-tail or two-tail test could be used with equivalent results.

a one-tail test should be utilized.

a two-tail test should be utilized.

None of these.

Question 50

TABLE 10-1

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

American Japanese

Sample size 211 100

Mean SSATL Score 65.75 79.83

Population Std. Dev. 11.07 6.41

Referring to Table 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers.

H0 : ? A – ? J ? 0 versus H1 : ? A – ? J < 0

H0 : ? A – ? J ? 0 versus H1 : ? A – ? J > 0

H0 : ? A – ? J = 0 versus H1 : ? A – ? J ? 0

H0 : X ? A – X ? J ? 0 versus H1 : X ? A – X ? J ? 0

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